Multi-Class and Multi-Task Strategies for Neural Directed Link Prediction

TL;DR

Directed Link Prediction must account for edge direction and bidirectionality, but traditional NDLP approaches trained on undirected existence signals fail to learn these aspects. The authors propose three strategies—MC-NDLP (four-class), MO-DLP (multi-objective with MGDA), and S-DLP (scalarization)—along with Simultaneous Splits to train NDLP-capable encoders across General, Directional, and Bidirectional tasks. Empirical results across Cora, CiteSeer, and Google show consistent gains in Directional and Bidirectional performance, with varying trade-offs on General DLP depending on the model and dataset. The work enables more robust directionality learning in GNNs and suggests applicability to knowledge graphs and other directed-graph tasks through coordinated multi-task training and task-split design.

Abstract

Link Prediction is a foundational task in Graph Representation Learning, supporting applications like link recommendation, knowledge graph completion and graph generation. Graph Neural Networks have shown the most promising results in this domain and are currently the de facto standard approach to learning from graph data. However, a key distinction exists between Undirected and Directed Link Prediction: the former just predicts the existence of an edge, while the latter must also account for edge directionality and bidirectionality. This translates to Directed Link Prediction (DLP) having three sub-tasks, each defined by how training, validation and test sets are structured. Most research on DLP overlooks this trichotomy, focusing solely on the "existence" sub-task, where training and test sets are random, uncorrelated samples of positive and negative directed edges. Even in the works that recognize the aforementioned trichotomy, models fail to perform well across all three sub-tasks. In this study, we experimentally demonstrate that training Neural DLP (NDLP) models only on the existence sub-task, using methods adapted from Neural Undirected Link Prediction, results in parameter configurations that fail to capture directionality and bidirectionality, even after rebalancing edge classes. To address this, we propose three strategies that handle the three tasks simultaneously. Our first strategy, the Multi-Class Framework for Neural Directed Link Prediction (MC-NDLP) maps NDLP to a Multi-Class training objective. The second and third approaches adopt a Multi-Task perspective, either with a Multi-Objective (MO-DLP) or a Scalarized (S-DLP) strategy. Our results show that these methods outperform traditional approaches across multiple datasets and models, achieving equivalent or superior performance in addressing the three DLP sub-tasks.

Figures (2)

• Figure 1: From a graph $G$ (top panel), for each task definition, green edges are the positive class and red edges are the negative class. In General DLP, any absent directed edge can be selected as negative. For Directionality prediction, unidirectional edges are positive, with their inverses as negatives. For Bidirectionality prediction, one direction of bidirectional edges is positive, and the reverse of unidirectional edges is negative.
• Figure 2: Performance difference of each proposed strategy compared to the baseline, measured in ROC-AUC (x100). Each bar represents the change in ROC-AUC - either an increase or decrease - when applying one of the proposed strategies to a specific sub-task, NDLP model, and dataset, relative to the same model's baseline performance. Scores are averaged over 5 runs. Error bars are omitted for visual clarity.